Why Autoencoder Weights Are Not Always Tied
We expect the decoder to learn anything meaningful without tying the weights because the loss function is calculated between the input and reconstructed output and training will minimize that loss. The untied autoencoder's decoder will learn to transform the embedding back into the input. Not tying the weights gives more representational power and also increases chances of overfitting.
If you are running into overfitting while training your autoencoder tying your weights is an option. It is a regularization method. Not tying them is fine if you are getting any overfitting or want to solve overfitting by an alternative method.